Question

PLZ HELP NO LINKS! WILL GIVE BRAINLIEST!

Answer 1

Answer:

t = 16.6

Step-by-step explanation:

In the formula:

$a = p(1 + r )^{t}$

A is the final amount, in this case is 11500 people. P is the initial amount, in this case is 6500 people. r is the growth rate, which in this case is 0.035 - we have to express it s a decimal, not a percent. And finally t is the time, which is the variable we want to find.

Let's clear t first and replace all these values at the end. To clear t we have to leave only the factor which exponent is t on one side of the equation. To do this we have to divide both sides by P:

$\frac{a}{p} = \frac{p}{p} (1 + r) ^{t} \\ \frac{a}{p} = (1 + r)^{t}$

Now we have to use the following rule for the exponents and logarithms:

${a}^{x} = b$

Apply logarithms on both sides:

$log( {a}^{x}) = log(b)$

By the exponents rule of logarithms

$x \: log(a) = log(b)$

For this problem we have:

$log \frac{a}{p} = log(1 + r)^{t} \\ log \frac{a}{p} =t \: . \: log(1 + r)$

Now we have to divide both sides by log(1+r) to clear t:

$log \frac{a}{p} = t \: . \: \frac{log(1 + r)}{log(1 + r)} \\ t = \frac{log \: \frac{a}{p} }{log(1 + r)}$

And finally we just have to replace the values into this equation we found: A = 11500, P = 6500 and r = 0.035:

$t = log \: \frac{11500}{6500} \\ log(1 + 0.035) \\ log \: \frac{23}{13} \\ t = log \: 1.035 \\ t = 16.6$

Answer 2

Answer:

24,831.28

Step-by-step explanation:

Brainliest pls